Question

Let $Z\sim N(0,a)$ with variance $a>0$. Show that the mgf of $Z^{2}$ is $M_Z^{2}(t)=\frac{1}{\sqrt{1-2at}}$

score 113 · Answer 1 · 2021-06-10 14:14:54

113

Views

Let $Z\sim N(0,a)$ with variance $a>0$. Show that the mgf of $Z^{2}$ is $M_Z^{2}(t)=\frac{1}{\sqrt{1-2at}}$

Published on 10 Jun 2021 - 14:14

score 393 · Answer 2 · 2021-06-15 10:06:40

393

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What is the moment generating function of this random variable?

Published on 15 Jun 2021 - 10:06

score 152 · Answer 3 · 2021-06-23 09:20:30

152

Views

Proving $e^{tx}$ is the only possibility for moment generating function

Published on 23 Jun 2021 - 9:20

score 50 · Answer 4 · 2021-06-24 16:15:20

50

Views

What is $E\left[\left(X_{i}-\overline{X}\right)^{3}\right]$?

Published on 24 Jun 2021 - 16:15

score 29 · Answer 5 · 2021-06-24 21:40:12

29

Views

Moment generating functions of $(1-X)/4$ where $X\sim U[0,1]$

Published on 24 Jun 2021 - 21:40

score 41 · Answer 6 · 2021-06-25 18:40:52

41

Views

Calculating the moment generating function: $t^k(1-p)^{k-1}p$

Published on 25 Jun 2021 - 18:40

score 643 · Answer 7 · 2021-07-02 18:52:46

643

Views

Where are the imaginary components in a moment generating function (MGF) of a distribution?

Published on 02 Jul 2021 - 18:52

score 115 · Answer 8 · 2021-07-03 16:23:50

115

Views

Solving for $s$ in $E[(1-h)^s]$ in terms of moments of $h$

Published on 03 Jul 2021 - 16:23

score 24 · Answer 9 · 2021-07-11 17:49:21

24

Views

Show that $M\left(t\right)$ is the expected number of values in the sample that lie between $\mu-t$ and $\mu+t$

Published on 11 Jul 2021 - 17:49

score 431 · Answer 10 · 2026-03-13 03:13:07

431

Views

Laplace transform of the Weibull distribution for $\kappa>1$

Published on 13 Mar 2026 - 3:13

score 58 · Answer 11 · 2021-08-05 15:27:06

58

Views

Can it ever be that for a random sample $X_1, ..., X_n$ we have that $\frac{1}{n}\Sigma_{i=1}^n x_i^2 \lt (\frac{1}{n}\Sigma_{i=1}^n x_i)^2$

Published on 05 Aug 2021 - 15:27

score 198 · Answer 12 · 2021-08-09 05:26:03

198

Views

Prove the Wald's identity using that $E[S_{N}]=M^{\prime}_{S_{N}}(0)$

Published on 09 Aug 2021 - 5:26

score 879 · Answer 13 · 2021-08-09 19:04:45

879

Views

Why are odd moments of Normal distribution equal to 0

Published on 09 Aug 2021 - 19:04

score 143 · Answer 14 · 2021-08-11 04:02:40

143

Views

Moment generating function of a discrete random variable that takes 0.5 or -0.5 with equal probabilities

Published on 11 Aug 2021 - 4:02

score 686 · Answer 15 · 2021-08-12 10:49:12

686

Views

Generating function of a random walk

Published on 12 Aug 2021 - 10:49

List Question

Let $Z\sim N(0,a)$ with variance $a>0$. Show that the mgf of $Z^{2}$ is $M_Z^{2}(t)=\frac{1}{\sqrt{1-2at}}$

What is the moment generating function of this random variable?

Proving $e^{tx}$ is the only possibility for moment generating function

What is $E\left[\left(X_{i}-\overline{X}\right)^{3}\right]$?

Moment generating functions of $(1-X)/4$ where $X\sim U[0,1]$

Calculating the moment generating function: $t^k(1-p)^{k-1}p$

Where are the imaginary components in a moment generating function (MGF) of a distribution?

Solving for $s$ in $E[(1-h)^s]$ in terms of moments of $h$

Show that $M\left(t\right)$ is the expected number of values in the sample that lie between $\mu-t$ and $\mu+t$

Laplace transform of the Weibull distribution for $\kappa>1$

Can it ever be that for a random sample $X_1, ..., X_n$ we have that $\frac{1}{n}\Sigma_{i=1}^n x_i^2 \lt (\frac{1}{n}\Sigma_{i=1}^n x_i)^2$

Prove the Wald's identity using that $E[S_{N}]=M^{\prime}_{S_{N}}(0)$

Why are odd moments of Normal distribution equal to 0

Moment generating function of a discrete random variable that takes 0.5 or -0.5 with equal probabilities

Generating function of a random walk

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